You've got to move like great-grandpa ... Mick Jagger performs with the Rolling Stones during the British Summertime Hyde Park concert in London on July 13, 2013. Photo: AFP

"The women in our family just tend to have children young, it runs in the genes," the new mum previously told Hello! magazine, adding that she's "very settled" for her age. The couple live in a converted barn in Cornwall, about 400 kilometres from London, the Daily Mail reported.

The father is Alex Key, 25, a chef. Jackson has a small homeopathy business, the Mail said.

New life follows tragedy ... Rolling Stones front man Mick Jagger and the late US stylist L'Wren Scott, who took her own life on March 17 in New York. Photo: AFP

Assisi is the older of Jade Jagger's two daughters with onetime partner Piers Jackson.

Jade, who is 42 and had Assisi at age 20, is herself pregnant, expecting a child next month with husband Adrian Fillary, a DJ and music promoter. The women were thrown a mother-daughter baby shower in March.

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"I imagine it's nice to be a great-grandad — although I'm not sure he likes the idea of getting old, or being called one," Assisi Jackson told Hello!. "I call him Mick — I wouldn't start calling him grandpa."

And it seems Jade Jagger, whose mother is Bianca Jagger, Mick's first wife, hasn't even considered it to be news.

Wife number two ... Texan model Jerry Hall and her then husband Mick Jagger at a fashion show in 1997. Photo: Reuters

"I think making Mick a grandfather obviously had a big impact," she told the Sunday Times of London back in November, "whereas, now, making him a great-grandfather is no longer particularly interesting."

That joint baby shower in mid-March, right around the 50th anniversary of the Stones' first album, was hosted by Mick's former common-law wife, Jerry Hall, who's reportedly been like a stepmother to Jade.

It was Mick's relationship with Jerry that spurred Bianca to file for divorce after seven years of marriage to the rock star, alleging adultery. Mick and Jerry were in a relationship for 23 years, which included an unofficial 1990 wedding in Bali. They split in 1999.

Model and grandmother Jade Jagger is expecting her own child in June with husband Adrian Fillary, a DJ and music promoter. Photo: Marco Del Grande

A source sniped to the Daily Mail at the time of the double baby shower that Hall was hosting the event in part "to have a little pop at Mick and at [his girlfriend] L’Wren [Scott] whom, to put it mildly, the children are not so keen on. They even call her the black spider."

Mere days later, Scott would be found hanged in her New York apartment. In the wake of her suicide, Mick and the rest of the Stones canceled tour dates in Australia and New Zealand. Those shows have since been rescheduled for October and November, and the band is set to start their tour in Adelaide on October 25.